Question

How do you figure out the number of combinations in a $4$ digit number ?

Answer 1

In the given question we are required to find out the number of combinations in $4$ digit numbers when we are given no additional information or conditions regarding the same. We must know that the first digit should not be zero before attempting such questions as then it would not be a $4$ digit number.

Complete step by step solution:
So, we are to create a $4$ digit number. So, we have $10$ digits with us to fill up the $4$ place values or positions in the $4$ digit number. But, we should remember that we cannot place a zero at the very first place value from the left as then the number would no longer be a $4$ digit number.
Hence, we have only $9$ numbers to choose from for leftmost place value in the four digit number. Then, we have $10$ numbers each to fill up the remaining three place values in the four digit number.
Now, we know that all the selections must be consecutive as they will form a four digit number. Hence, we will multiply the ways of selecting the number for the place values and obtain our final answer.
Therefore, the number of combinations in $4$ digit number $= 9 \times 10 \times 10 \times 10$
$= 9000$
Therefore, there are $9000$ ways or combinations to form a $4$ digit number.

Note:
In such a problem, one must know the multiplication rule of counting as consequent events are occurring. One must take care while doing the calculations and should recheck them so as to be sure of the final answer.